Suboptimality of Lloyd's algorithm. Consider the following data set consisting of five points in R1: 10, 8, 0, 8, 10.

We would like to cluster these points into k = 3 groups.

(a) What is the optimal k-means solution? Give the locations of the centers as well as the k-means

cost.

(b) Suppose we call Lloyd's k-means algorithm on this data, with k = 3 and with initialization 1 = 10, 2 = 8, 3 = 0. What is the final set of cluster centers obtained by the algorithm? What is the k-means cost of this set of centers?